Call the impedance given by the top part of
the circuit *Z*_{1} and the impedance given by the
bottom part *Z*_{2}.

We see that *Z*_{1} = 70 + 60*j* Ω and
*Z*_{2} = 40 − 25*j* Ω

So

`Z_T=(Z_1Z_2)/(Z_1+Z_2)`

`=((70+60j)(40-25j))/((70+60j)+(40-25j))`

`=((70+60j)(40-25j))/(110+35j)`

(Adding complex numbers should be done in rectangular form.)

Now, we convert everything to polar form and then multiply and divide as follows:

`Z_T =((70+60j)(40-25j))/(110+35j)`

`=((92.20/_40.60^text(o))(47.17/_-32.01^text(o)))/(115.4/_17.65^text(o))`

(We do the product on the top first.)

`=((92.20xx47.17)/_(40.60^text(o)-32.01^text(o)))/(115.4/_17.65^text(o))`

`=(4349.074/_8.59^text(o))/(115.4/_17.65^text(o))`

(Now we do the division.)

`=(4349.074)/115.4/_(8.59^text(o)-17.65^text(o))`

`=37.69/_-9.06^text(o)`

(We convert back to rectangular form.)

`=37.22-5.93j`

(When multiplying complex numbers in polar form, we multiply the *r* terms (the numbers out the front) and add the angles. When dividing complex numbers in polar form, we divide the *r* terms and subtract the angles. See the Products and Quotients section for more information.)

So we conclude that the combined impedance is

`Z_T = 37-5.9j\ Omega`

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